Log question

[maggie0160]

Can someone tell me if I am right or in the right direction?

Log [ (AB)) /(CD) ] = log A - log B - log C - log D

 

[soroban]

Hello, maggie0160!

Can someone tell me if I am right or in the right direction?

\(\displaystyle \log\left(\frac{AB}{CD}\right) \:= \:\log A\,-\,\log B\,-\,\log C\,-\,\log D\) . . . . not quite
. . . . . . . . . . .↑

\(\displaystyle \log\left(\frac{AB}{CD}\right) \:= \:\log(AB)\,-\,\log(CD)\)

. . . . . . . . .\(\displaystyle = \\log A\,+\,\log B)\ -\ (\log C\,+\,\log D)\)

. . . . . . . . .\(\displaystyle = \:\log A\,+\,\log B\,-\,\log C\,-\,\log D\)